Title

On The Choice Of Auxiliary Linear Operator In The Optimal Homotopy Analysis Of The Cahn-Hilliard Initial Value Problem

Keywords

Auxiliary linear operator; Cahn-Hilliard equation; Convergence control parameter; Homotopy analysis method

Abstract

Analytical solutions for the Cahn-Hilliard initial value problem are obtained through an application of the homotopy analysis method. While there exist numerical results in the literature for the Cahn-Hilliard equation, a nonlinear partial differential equation, the present results are completely analytical. In order to obtain accurate approximate analytical solutions, we consider multiple auxiliary linear operators, in order to find the best operator which permits accuracy after relatively few terms are calculated. We also select the convergence control parameter optimally, through the construction of an optimal control problem for the minimization of the accumulated L 2-norm of the residual errors. In this way, we obtain optimal homotopy analysis solutions for this complicated nonlinear initial value problem. A variety of initial conditions are selected, in order to fully demonstrate the range of solutions possible. © 2013 Springer Science+Business Media New York.

Publication Date

1-1-2014

Publication Title

Numerical Algorithms

Volume

66

Issue

2

Number of Pages

269-298

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11075-013-9733-8

Socpus ID

84902000877 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84902000877

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